Symmetric extension of two-qubit states

Publication Type:
Journal Article
Physical Review A - Atomic, Molecular, and Optical Physics, 2014, 90 (3)
Issue Date:
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© 2014 American Physical Society. A bipartite state ρAB is symmetric extendible if there exists a tripartite state ρABB′ whose AB and AB′ marginal states are both identical to ρAB. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, one-way distillation of Einstein-Podolsky-Rosen pairs, one-way distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any two-qubit quantum state ρAB; specifically, tr(ρB2)≥tr(ρAB2)-4detρAB. As a special case we solve the bosonic three-representability problem for the two-body reduced density matrix.
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